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package class_2023_05_3_week;
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// 来自学员问题
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// 假设每一次获得随机数的时候，这个数字大于100的概率是P
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// 尝试N次，其中大于100的次数在A次~B次之间的概率是多少?
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// 0 < P < 1, P是double类型
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// 1 <= A <= B <= N <= 100
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public class Code02_More100TimesBetweenAB {
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public static double probability(double P, int N, int A, int B) {
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double[][] dp = new double[N + 1][N + 1];
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for (int i = 0; i <= N; i++) {
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for (int j = 0; j <= N; j++) {
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dp[i][j] = -1;
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}
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}
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double ans = 0;
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for (int j = A; j <= B; j++) {
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ans += process(P, 1D - P, N, j, dp);
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}
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return ans;
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}
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// 获得随机数大于100的概率是more
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// 获得随机数小于等于100的概率是less
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// 还有i次需要去扔
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// 扔出大于100的次数必须是j次
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// 返回概率
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public static double process(double more, double less, int i, int j, double[][] dp) {
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if (i < 0 || j < 0 || i < j) {
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return 0D;
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}
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// i >= 0 & j >= 0 & i >= j
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if (i == 0 && j == 0) {
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return 1D;
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}
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// i < 0
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// i == 0 j > 0
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// i == 0 j < 0
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// i == 0 j == 0
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// 如果是上面四种情况，都提前返回了
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// i > 0 & i >= j
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if (dp[i][j] != -1) {
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return dp[i][j];
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}
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// 1) > 100 情况，more * (i - 1, j - 1)
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// 2) <= 100 情况 , less * (i - 1, j)
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// 总体达成的概率 = 1) + 2)
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double ans = more * process(more, less, i - 1, j - 1, dp) + less * process(more, less, i - 1, j, dp);
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dp[i][j] = ans;
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return ans;
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}
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public static void main(String[] args) {
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double P = 0.6;
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int N = 100;
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int A = 30;
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int B = 50;
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System.out.println(probability(P, N, A, B));
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}
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}
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